The present invention relates to a computerized method for creating a two-dimensional or three-dimensional finite element model of a rubber composite comprising a rubber matrix and fillers, capable of improving the accuracy of computer simulations and reducing the processing time for creating the finite element model.
In recent years, various computer simulations utilizing a finite element method are widely employed.
In such a simulation, in order that a computer can deal with the analysis object, the analysis object is discretized into a finite number of elements to create a finite element model of the analysis object. The finite element model is provided with various characteristics, and a deformation calculation in which displacements of nodes of the elements are calculated, is made.
Finite element models may be created by various methods.
In the case that the analysis object is a rubber composite (b) in which fillers (c) are dispersed in a rubber matrix (d) as shown in FIG. 14, and to be created is a two-dimensional finite element model, as shown in FIG. 15(a) for example, regions (h) in which the filler (c) reside and a region (g) in which the rubber matrix (d) resides are defined in a predetermined two-dimensional space (i), and a finite element model (a) in which these regions are each discretized by the use of triangular elements (e) is created.
Meanwhile, as the rubber has incompressibility, such incompressible material characteristic is defined on each of the triangular elements (e) of the rubber matrix's region (g). Therefore, when a side of the triangular element (e) of the rubber matrix's region (g) is connected to the region (h) of the filler which is defined as having a higher rigidity than the rubber matrix, the triangular element (e) is restrained and the degrees of freedom of its deformation is greatly decreased.
As a result, in the part (or elements) of the rubber matrix abutting the fillers, the rigidity of the rubber matrix is calculated as if it is higher than it really is, and thereby the simulation accuracy is decreased.
On the other hand, in a finite element model (a) made up of quadrilateral elements (f) as shown in FIG. 15(b), even if a side of the quadrilateral element (f) of the rubber matrix's region (g) is connected to the region (h) of the filler, as the degrees of freedom of deformation of the quadrilateral element is high when compared with the triangular element (e) as shown in FIG. 15(a), there is less possibility of the above-mentioned overestimation of the rigidity in the abutting part.
In the case of a finite element model made up of quadrilateral elements (f), in comparison with the triangular elements (e), it is difficult for the computer or meshing software to automatically divide a region of a filler having a round shape into quadrilateral elements, and manual procedures are necessitated, therefore, the creating the finite element model takes a lot of time and effort.
This is also true in the case of a three-dimensional finite element model using hexahedron elements.
Namely, to create a three-dimensional finite element model made up of tetrahedral elements is relatively easy, but there is a possibility of the overestimation of the rigidity of the rubber matrix in the part abutting the fillers because the degrees of freedom of deformation of a tetrahedral element is low, and if one of four faces of a tetrahedral element is connected to the region of the filler, the degrees of freedom of its deformation is greatly decreased.
If a three-dimensional finite element model made up of hexahedron elements is used, there is less possibility of the overestimation of the rigidity because the degrees of freedom of deformation of a hexahedron element is relatively high.
However, the creating the finite element model takes more complicated tasks than 2D and a lot of time.